This study is designed to determine the long-term effects of 3 treatments (two classes of anti-inflammatory agents (budesonide or nedocromil) and placebo over a 5 to 6-1/2 year period. Every patient will use an intermittent short acting B2-agonist (albuterol). Children, aged 5-12 (one third from ethnic minority groups), who have had asthma symptoms for nine or more months with chronic symptoms for at least 6 months during the past year will be studied.